Year: 2020
Author: Hongbo Guan, Yong Yang, Huiqing Zhu
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 527–544
Abstract
In this paper, we investigate a mixed finite element method (MFEM) for the elliptic optimal control problems (OCPs) with a distributive control. The state variable and adjoint state variable are approximated by the conforming rectangular $Q_{11}+Q_{01}\times Q_{10}$ elements pair. The discrete B-B condition is satisfied automatically, which is usually considered to be the key point of the MFEM. The control is then obtained by the orthogonal projection through the adjoint state. Optimal orders of convergence are derived for the above mentioned variables. Furthermore, supercloseness and superconvergence results are also established under certain reasonable regularity assumptions. Some numerical results are provided to verify the theoretical analysis. At last, the proposed method is extended to some other low order conforming and nonconforming elements.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0019
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 527–544
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: MFEMs OCPs optimal order error estimates supercloseness and superconvergence.